Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations

It is shown that the action of a special rank 2 or rank 3 Darboux transformation, calledtransference, upon a pair of commuting ordinary differential operators of orders 4 and 6 implements the Abelian sum on their elliptic joint spectrum. A consequence of this is that, under the deformation of these commuting operators by the KP flow, every rank 2 KP solution corresponds to a solution of the Krichever-Novikov (KN) equation, and vice versa, with the transference process providing the correspondence between (2+1) and (1+1) dimensions. For a singular joint spectrum, it is further shown that transference at the singular point produces a correspondence between solutions of the singular KN equation and those of the KdV equation. These correspondences are illustrated by considering examples of a nondecaying rational KdV or Boussinesq solutions and the corresponding rational, singular-KN and rational KP solutions which the transference process generates.     

EFK方程一个新的低阶非协调混合有限元方法的高精度分析

对Extended Fisher-Kolmogorov(EFK)方程,利用EQ_1~(rot)元和零阶RaviartThomas(R-T)元建立了一个新的非协调混合元逼近格式.首先,证明了半离散格式逼近解的一个先验估计并证明了逼近解的存在唯一性.在半离散格式下,利用上述两种元的高精度分析结果以及这个先验估计,在不需要有限元解u_h属于L~∞的条件下,得到了原始变量u和中间变量v=-?u的H~1-模以及流量p=u的(L~2)~2-模意义下O(h~2)阶的超逼近性质.同时,借助插值后处理技术,证明了上述变量的具有O(h~2)阶的整体超收敛结果.其次,建立了一个新的线性化向后Euler全离散格式并证明了其逼近解的存在唯一性.另一方面,通过对相容误差和非线性项采取与传统误差分析不同的新的分裂技巧,分别导出了以往文献中尚未涉及的关于u和v在H~1-模以及p在(L~2)~2-模意义下具有O(h~2+τ)阶的超逼近性质,进一步地,借助插值后处理技术,得到了上述变量的整体超收敛结果.这里h和τ分别表示空间剖分参数和时间步长.最后,给出了一个数值算例,计算结果验证了理论分析的正确性.     

A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM

In this paper, a novel method is proposed for solving nonlinear two-point boundary value problems (BVPs). This method is based on a combination of the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). A major advantage of this method over standard ADM is that it can avoid unnecessary computation in determining the unknown parameters. The proposed method can be applied to singular and nonsingular BVPs. Numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two-point boundary value problems.     

A novel scheme for the design of backstepping control for a class of nonlinear systems

A novel scheme is proposed for the design of backstepping control for a class of state-feedback nonlinear systems. In the design, the unknown nonlinear functions are approximated by the neural networks (NNs) identification models. The Lyapunov function of every subsystem consists of the tracking error and the estimation errors of NN weight parameters. The adaptive gains are dynamically determined in a structural way instead of keeping them constants, which can guarantee system stability and parameter estimation convergence. When the modeling errors are available, the indirect backstepping control is proposed, which can guarantee the functional approximation error will converge to a rather small neighborhood of the minimax functional approximation error. When the modeling errors are not available, the direct backstepping control is proposed, where only the tracking error is necessary. The simulation results show the effectiveness of the proposed schemes.     

关于二阶完全非线性抛物组的差分格式

则称二阶完全非线性组(1)是一致抛物的.我们在矩形域Q_T={0≤x≤l,0≤t≤T}(l>0,T>0)上研究方程组(1)满足边界条件     

Self-dual Sheaves on Reductive Borel—Serre Compactifications of Hilbert Modular Surfaces

The main theorem of this article asserts that the category of self-dual sheaves compatible with the intersection chain sheaves (for upper/lower middle perversity) on the reductive Borel—Serre compactification of a Hilbert modular surface is nonempty. Also we prove that the direct image of such a sheaf under the canonical map to the Baily—Borel compactification is isomorphic (in the derived category) to the intersection chain sheaf for upper and lower middle perversity. As a consequence of the main theorem, there exist characteristic L-classes of these sheaves in the rational homology of . In fact, these classes do not depend on the choice of a self-dual sheaf and hence are invariants of the compactification .     

Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order

The general difference schemes for the first boundary problem of the fully nonlinear parabolic systems of second order f(x, t, u, u_x, u_{xx}, u_t) = 0 are considered in the rectangular domain Q_T = {0 ≤ x ≤ l, 0 ≤ t ≤ T}, where u(x, t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m ≥ 1 for (x, t) ∈ Q_T and u, p, r, q ∈ R^m. The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a priori estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear parabolic systems are also obtained.     

Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters

A spatially and temporally discrete numerical approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. Finite-dimensional difference equation state approximations are constructed using a cubic spline-based, Galerkin method and the Padé rational function approximations to the exponential. A sequence of approximating identification problems result, the solutions of which are shown to exist and, in a certain sense, approximate solutions to the original identification problem. Numerical results for two examples, one involving the modeling of biological mixing in deep sea sediment cores, and the other, the estimation of transport parameters for indoor mixing, are discussed. In both examples, the identification is based upon actual experimental data.Parts of the research were carried out while the authors were visitors at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, Virginia, which is operated under NASA Contracts No. NAS1-17070 and No. NAS1-17130.Research supported in part by NSF Grant MCS-8205355, AFOSR Contract 81-0198 and ARO Contract ARO-DAAG-29-K-0029.     

抛物型方程一个新的非协调混合元超收敛性分析及外推

本文研究了抛物型方程在新混合元格式下的非协调混合有限元方法. 在抛弃传统有限元分析的必要工具-Ritz 投影算子的前提下,直接利用单元的插值性质,运用高精度分析和对时间t的导数转移技巧,借助于插值后处理技术,分别导出了关于原始变量u的H¹-模和通量p=▽u在L²-模下的O（h²）阶超逼近性质和整体超收敛. 进一步,通过构造合适的辅助问题,运用Richardson 外推格式,得到了具有更高精度O（h³）阶的外推结果. 最后,给出了一些数值结果验证了理论分析的正确性.     

Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features

The relationship between viral load and CD4 cell count is one of the interesting questions in AIDS research. Statistical models are powerful tools for clarifying this important problem. Partially linear mixed-effects (PLME) model which accounts for the unknown function of time effect is one of the important models for this purpose. Meanwhile, the mixed-effects modeling approach is suitable for the longitudinal data analysis. However, the complex process of data collection in clinical trials has made it impossible to rely on one particular model to address the issues. Asymmetric distribution, measurement error and left censoring are features commonly arisen in longitudinal studies. It is crucial to take into account these features in the modeling process to achieve reliable estimation and valid conclusion. In this article, we establish a joint model that accounts for all these features in the framework of PLME models. A Bayesian inferential procedure is proposed to estimate parameters in the joint model. A real data example is analyzed to demonstrate the proposed modeling approach for inference and the results are reported by comparing various scenarios-based models.     

WARSYP: a robust modeling approach for water resources system planning under uncertainty

In this work we present a solution procedure for multiperiod water resources system planning, where the aim is to obtain the optimal policy for water resources utilization under uncertainty. The target levels to be achieved are related to the following parameters: reservoir capacity, hydropower demand and other demand uses for urban, industrial, irrigation, ecological and other purposes. The approach allows for the conjunctive use of surface systems together with groundwater. The hydrological exogenous inflow and demand of different kinds are considered via a scenario analysis scheme due to the uncertainty of the parameters. So, a multistage scenario tree is generated and, through the use of full recourse techniques, an implementable solution is obtained for each scenario group at each stage along the planning horizon. A novel scheme is presented for modeling the constraints to preserve the reserved stored water in (directly and non-directly) upstream reservoirs to satisfy potential future needs in demand centers at given time periods. An algorithmic framework based on augmented Lagrangian decomposition is presented. Computational experience is reported for the deterministic case.     

Optimal designs for weighted rational models

This paper is concerned with constructing optimal designs for rational models which are used for modeling problems in Agriculture and other disciplines. Homoscedastic and weighted models are considered. An analytical characterization of these designs is obtained as zeros of a polynomial solution of a second order differential equation.     

Hole-Size Effects in Pultruded Composites

The stress-gradient effects on the fracture strength of materials have been recognized for a long time. In metals, Neuber's elementary block theory has been used to explain why the actual strength reduction due to notches is less than that indicated by the stress-concentration factor. In fiber-reinforced composites, the same concept was renamed as the hole-size effect, giving rise to a point-stress characteristic dimension and an average-stress characteristic dimension.     

Scaling Invariants and Symmetry Reduction of Dynamical Systems

Scalings form a class of group actions that have theoretical and practical importance. A scaling is accurately described by a matrix of integers. Tools from linear algebra over the integers are exploited to compute their invariants, rational sections (a.k.a. global cross-sections), and offer an algorithmic scheme for the symmetry reduction of dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models.     

Indirect identification of continuous-time delay systems from step responses

In this paper, an indirect identification scheme is proposed for identifying the parameters of the continuous-time first-order plus time delay (FOPTD) model and the second-order plus time delay (SOPTD) model from step responses. Unlike the existing direct identification scheme, which identifies the parameters of the continuous-time FOPTD and SOPTD models directly from the continuous-time step response data, the proposed indirect scheme is to pre-identify discrete-time FOPTD and SOPTD models from the discretized continuous-time step response input–output data, then convert the obtained discrete-time models to the desirable continuous-time models. The proposed method is then extended to identify the afore-mentioned models from the step responses of the systems contaminated with input noise and constant output disturbance. The proposed simple alternative method exhibits good estimation performances in both the time domain and the frequency domain. Illustrative examples are presented to demonstrate the effectiveness of the proposed scheme.     

Negotiation-based collaborative planning between supply chains partners

It is often proposed that operations planning in supply chains can be organized in terms of a hierarchical planning system. However, the hierarchical approach assumes a single, centralized planning task for synchronizing operations across the supply chain. As central coordination can usually be realized only for isolated parts of an overall supply chain, the question arises whether there are alternative ways of coordination.In this paper we propose a non-hierarchical, negotiation-based scheme which can be used to synchronize plans between two independent supply chain partners linked by material flows. Assuming that plans are generated based upon mathematical programming models, we show how modified versions of these models can be utilized for evaluating material orders or supplies proposed by the supply chain partner and for generating counter-proposals. Resulting is an iterative, negotiation-like process which establishes and subsequently improves a consistent overall plan. Computational tests suggest that the scheme comes close to optimal results as obtained by central coordination.     

Parameter–identification of macroscopic material models based on virtual testing of given material mesostructures

For many heterogeneous materials such as composites and polycrystals, the material modeling for the constituents on a representative mesoscale can be considered as known, including concrete values of their inherent material parameters. Typical examples are isotropic elastic–plastic models for the constituents of composites or anisotropic crystal–plasticity models for the grains of polycrystals. This knowledge can be exploited with regard to the modeling of the homogenized macroscopic response. In particular, parameters in macroscopic models may be identified by virtual experiments provided by a computational deformation–driving of representative mesostructures. This paper outlines the general concept for the parameter–identification of macroscopic materialmodels based on the virtual testing of given material mesostructures. The virtual test data are obtained in the form of multi–dimensional stress–strain paths by applying different deformation gradients to a given mesostructure. After specifying a corresponding macroscopic material model covering the observed effects on the macroscale, the material parameters are identified by a least–square–type optimization procedure that optimizes the macroscopic material parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

含多个任意参数的广义变分原理及换元乘子法

弹性力学变分原理的泛函变换可分为三种格式:Ⅰ、放松格式,Ⅱ、增广格式,Ⅲ、等价格式. 根据格式Ⅲ,提出含多个任意参数的广义变分原理及其泛函表示式,其中包括:以位移u为一类泛函变量的多参数广义变分原理;以位移u和应力σ为二类泛函变量的多参数广义变分原理;以位移u和应变ε为二类泛函变量的多参数广义变分原理;以位移u应变ε和应力σ为三类泛函变量的多参数广义变分原理.由这些原理可得出等价泛函一系列新形式,此外,通过参数的合理选择,可构造出一系列有限元模型. 本文还讨论了拉氏乘子法“失效”问题,指出“失效”现象产生的原因,提出乘子法“恢复有效”的作法——换元乘子法.     

Infinitesimal,first order bendings of smooth,convex surfaces of revolution subject to conic,sleeve-like constraints along the boundary

We prove that on a closed, smooth, convex surface of revolution , whose poles are not flattening points, there exists only a countable set of parallels _n. Each of these parallels cuts surface into two parts so that one of the parts, , admits nontrivial, infinitesimal bendings in the process of which all the points of its boundary _n are displaced on a preassigned, conic sleeve K that is coaxial with the surface. The sequence of such parallels _n converges to parallel ^*, which has the following properties: 1) the tangent cone to surface along ^* is orthogonal to sleeve K; 2) surface , cut off from surface by parallel ^*, has rigidity of first order in the indicated class of bendings.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 3–8, 1990.     

一种计算工作时间参数新方法

为了编制和优化施工进度计划,计算构成施工项目的各项工作最早开始时间、最迟开始时间、最早完成时间、最迟完成时间、总时差和自由时差等时间参数十分重要.提出了一种计算工作时间参数新方法.该方法以工作完成时间为决策变量,通过建立和求解线性规划模型来得到各种工作时间参数.其建模思路清晰,不需绘制网络图,能用通用办公软件EXCEL求解.模拟计算表明,用该方法与用标准网络计划技术计算出的工作时间参数完全一致.